Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 → Mechanics ↓


Rotational motion


Rotational motion is a fascinating concept in physics that deals with the motion of objects moving around a fixed axis. Unlike linear motion, where objects move in a straight line, rotational motion involves circular paths. Understanding this kind of motion is important for understanding how many systems work, from planets orbiting stars to wheels that propel vehicles, and even the rotation of fan blades.

Basic concepts of rotational motion

Before delving deeper into rotational motion, let us understand some basic concepts and terminologies that are essential to understand this topic:

Axis

The axis of rotation is an imaginary line around which an object rotates. It can be internal, like the axle in a wheel, or external, like the Earth rotating around the Sun.

Angular displacement

Angular displacement refers to the change in angle when an object rotates around an axis. It is usually measured in radians. For example, if a wheel rotates from a reference point O to A, the angular displacement is the angle between OA and the original line position.

Hey A

Angular velocity

Angular velocity, often represented by ω, is the rate at which an object rotates. It is the change in angular displacement relative to time. The unit is radians per second (rad/s).

ω = frac{Delta theta}{Delta t}

In this formula, Δθ is the angular displacement and Δt is the change in time.

Angular acceleration

Angular acceleration is the rate of change of angular velocity over time. It is represented by the symbol α and is measured in radians per second squared (rad/s²).

α = frac{Delta omega}{Delta t}

Here, Δω is the change in angular velocity and Δt is the time during which the change occurs.

Understanding rotational motion with examples

Example 1: Rotating wheel

Imagine a bicycle wheel rotating around its axis. The axis acts as the axis of rotation, and any point on the wheel follows a circular trajectory around this axis. If you place a mark on the rim of the wheel, you can trace the path and note how the angle changes over time.

Example 2: A merry-go-round

Consider a merry-go-round in a playground. As it rotates, a person sitting on it follows a circular path. The rotational motion of a merry-go-round can be described using angular displacement, velocity, and acceleration. The principal axis of rotation is typically the central axis passing through the center of the merry-go-round.

M Hey

Equations of rotational motion

Just as there are equations of motion for linear motion, there are equations for rotational motion as well. Here are some important equations, which are similar to the equations of linear motion:

Angular kinematics equations

  • Final angular velocity given initial angular velocity and angular acceleration: 
    ω = omega_0 + alpha t
  • Angular displacement given initial angular velocity and time: 
    θ = omega_0 t + frac{1}{2} alpha t^2
  • Square of final angular velocity given initial angular velocity, angular acceleration and angular displacement: 
    omega^2 = omega_0^2 + 2alphatheta

These equations allow you to analyze rotational motion in the same way you analyze linear motion using kinematics.

Dynamics of rotational motion

To fully understand rotational motion, it is important to look at the forces that cause the motion. Here are some important concepts:

Torque

Torque is the rotational equivalent of force. It measures how much a force applied to an object rotates that object. The greater the torque, the greater the tendency of the object to rotate. Torque is calculated as follows:

τ = r cdot F cdot sin(theta)

In this formula, τ is the torque, r is the distance from the axis of rotation to the location where the force is applied, F is the magnitude of the force, and θ is the angle between the force vector and the arm.

Moment of inertia

Moment of inertia is a measure of an object's resistance to a change in rotation. It depends on how the mass is distributed with respect to the axis of rotation. In general, the distribution of mass determines how difficult it is to change an object's rotational speed:

I = sum m_i r_i^2

Here, I is the moment of inertia, m_i is the mass of each element, and r_i is the distance of each element from the axis of rotation.

R2 R1

Newton's second law for rotational motion

Newton's second law for rotational motion relates the net torque applied to an object to its angular acceleration:

τ = I cdot alpha

This equation states that the net torque τ acting on an object is equal to the product of the moment of inertia I and the angular acceleration α. This is equivalent to the linear momentum F = m cdot a.

Work, power and energy in rotational motion

Similar to linear motion, rotational motion involves the concepts of work, power, and energy:

  • Rotational work: defined as the product of torque and angular displacement: 
    W = tau cdot theta
  • Rotational kinetic energy: Similar to linear kinetic energy, but for rotation: 
    KE_{rot} = frac{1}{2} I omega^2
  • Power: The rate at which work is done or energy is transferred: 
    P = tau cdot omega

Applications of rotational motion

Flywheels

Flywheels are devices specifically designed to store rotational energy. They use the principles of rotational motion, particularly the moment of inertia, to retain energy and distribute it when needed. Engineers can effectively manage energy distribution in machines, especially in vehicles, by using flywheels.

Gyroscope

Gyroscopes are another fascinating application of rotational motion. These devices maintain orientation due to angular momentum. They are used for orientation purposes in navigation systems, aircraft, and even smartphones.

Game

Rotational dynamics are heavily used in activities such as diving, gymnastics, and figure skating. Athletes often twist their bodies in certain ways to control their motion and achieve desired results.

Final thoughts

Rotational motion is a vital component of the physical world. From the simple turn of a wheel to the grand dance of celestial bodies, understanding this motion helps explain how force and energy interact in various systems. Studying these concepts gives us the tools to manipulate rotational motion for many applications, improving the way we design and interact with technology and nature.


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Rotational motion

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